FIG. 1 illustrates a system for transmission of complex symbols {dn}nεN emitted by a symbols source. This transmission system comprises a modulator, a send filter, a transmission medium, a reception filter, a demodulator, an adder introducing Gaussian white noise samples {Wn}nεN and a sampler with a sampling period T. The modulator, send filter, transmission medium, reception filter and demodulator assembly forms a discrete equivalent transmission channel generating inter-symbol interferences (ISI). The transmission system outputs a sequence of complex symbols {rn}nεN defined by the following relation:
                              r          n                =                                            ∑                              k                =                                                      L                    1                                    +                  1                                                            L                2                                      ⁢                                                            Γ                  k                                ⁡                                  (                  n                  )                                            ⁢                              d                                  n                  -                  k                                                              +                      w            n                                              (        1        )            
where (Γ−L1+1(n), . . . , Γ0(n), . . . , ΓL2(n)) are coefficients (possibly complex) of the equivalent discrete transmission channel at time n, and L2 and L1−1 are respectively the past and future number of complex symbols generating the interference on the current complex symbol.
The equivalent discrete transmission channel transfer function that inputs inter-symbol interference is as follows, at time n:
                                          H            n                    ⁡                      (            f            )                          =                              ∑                          k              =                                                L                  1                                +                1                                                    L              2                                ⁢                                                    Γ                k                            ⁡                              (                n                )                                      ⁢                          exp              ⁡                              (                                                      -                    j2                                    ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  fkT                                )                                                                        (        2        )            
where T is the time period between two consecutive complex symbols in the sequence of complex symbols {rn}nεN.
For simplification reasons, the transfer function Hn(f) is denoted H(f) in the remainder of the description.
In equations (1) and (2), it is assumed that the pulse response of the equivalent discrete transmission channel (corresponding to the inverse Fourier transform of the transfer function) is defined by L=L1+L2 coefficients.
One of the best known inter-symbol interference cancellers is described in the document entitled “Adaptive Cancellation of Inter-symbol Interference for Data Transmission” by A. Gersho and T. L. Lim, Bell Systems technical journal, Vol. 11, No. 60, pp. 1997-2021, November, 1981.
A diagram of the structure of this inter-symbol interference canceller is shown in FIG. 2 of this application.
This interference canceller comprises a first filter 10 called the front filter, to process the sequence of complex symbols {rn}nεN, a second filter 20 called the back filter to process a sequence of complex symbols {{tilde over (d)}n}nεN, and a subtractor circuit 30 to subtract the output from filter 20 from the output from filter 10. The subtractor circuit 30 outputs a sequence of complex symbols {{tilde over ({tilde over (d)}n}nεN from which the inter-symbol interferences generated by the transmission channel have been eliminated.
The sequence {{tilde over (d)}n}nεN represents either complex symbols sent through the transmission channel by the sending source if the system uses a learning sequence, or complex symbols that are an estimate of complex symbols emitted by the sending source. In the second case, the sequence of symbols {{tilde over (d)}n}nεN is provided by another device in the receiver, for example a transverse linear equaliser or a maximum probability equaliser.
For generalisation reasons, it is assumed that the transmission channel varies in time. Therefore, the coefficients of the pulse response are not standardised. We then obtain the following relation:
            ∑              k        =                              L            1                    +          1                            L        2              ⁢                                                Γ            k                    ⁡                      (            n            )                                      2        =            α      n        .  It is also assumed that the signal sent has a unit power, and therefore that the variance σd2 of symbols sent is equal to 1. With this assumption, αn is equal to the estimated power of the transmission channel.
The filter 10 of the device converges towards a filter tuned to the transmission channel. The optimum coefficients, for example in the sense of the minimum mean quadratic error criterion, of filter 10 are therefore the coefficients of the filter tuned to the transmission channel. Therefore, the optimum transmission function of this filter is equal to
      1                  σ        w        2            +              α        n              ⁢  H  *            (      f      )        .  H*(f) denotes the conjugate of the transfer function H(f) and σw2 denotes the variance of the Gaussian noise.
The filter 20 is designed to reconstruct inter-symbol interferences present at the output from filter 10. Therefore the filter 20 converges to a filter with transfer function equal to
      1                  σ        w        2            +              α        n              ⁢            (                                                              H              ⁡                              (                f                )                                                          2                -                  α          n                    )        .  Therefore the filters 10 and 20 represent sizes L and 2L−1 respectively. The filter coefficients are output as the processing is being done, either using a channel estimate algorithm or using a matching algorithm designed to minimise a given optimisation criterion.
The invention is based on a search for inter-symbol interference cancellers designed to reduce the size of filters necessary for their use, so that degradation caused by an excessive number of coefficients can be limited and to reduce the coefficient convergence time.